where is this "Platonic world", where the plans for the Universe are stored until they are needed? For if the map/plan exists, and this Platonic world is where it exists, then where is this Platonic world? Your surmise seems to rest upon your having an answer to this question, doesn't it? :wink: :chin: — Pattern-chaser
To believe that maths was discovered is to mistake the map for the territory. [ It also avoids the rather obvious criticism that there is nowhere in the real universe that we can point to and say "there's maths" or "Oh, look, there's a sine wave". ] — Pattern-chaser
Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences. Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate.
Standard readings of mathematical claims entail the existence of mathematical objects. But, our best epistemic theories seem to debar any knowledge of mathematical objects.
there is exists this very simple "object" [...] and a map, or plan [...] made of all possible mathematical objects that can be built. — Mephist
in order to map and understand what is 'out there' - creating the map, that you say is 'mistaken for the territory' - maths itself has proven indispensable. And maths, furthermore, enables science to predict and discover things which could never be known by observation alone. — Wayfarer
So I think it's not feasible to argue that the relationship between mathematics and nature is merely fortuitous. — Wayfarer
number is real, but transcendent in respect to the physical — Wayfarer
And where does this map exist? Where is the 'place' where this map is stored and retained, ready for later use? The only thing I know of that can store an idea is a conscious mind. Perhaps there is some other container that can also achieve this, but what and where is it, this store? — Pattern-chaser
Maths is indispensable because it's a good and well-crafted tool. It's useful. — Pattern-chaser
We created maths to be what it is, to do what it does. We made this valuable mapping tool on purpose — Pattern-chaser
I think I answered your initial assertion of this point, in terms of the argument that through maths, we can discover many real principles and properties, on the basis of which you can then invent all kinds of devices - like the LHC above. But the things discovered, like natural laws, are plainly not invented by us, and their mathematical qualities are likewise there to be found. — Wayfarer
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